As a state senator, Braden was also a member of the executive committee of the Democratic National Committee in Washington, D.C. From 1986 to 1994, he was an advisor to Mayor Barthelemy, whom he had worked to elect. Braden was active in the black political organization COUP, which dominated the Seventh Ward. COUP was in conflict with another group LIFE, loyal to former Mayor Ernest Morial, the first African-American in the mayoral office, and to Morial's son, Marc Morial, another later mayor. Accustomed to taking passionate positions, Braden was once involved in a fist fight with former city councilman and police chief Joe Giarrusso; the confrontation occurred at the original Ruth’s Chris Steak House on Broad Street in New Orleans.[1]

In his later years, Braden was a lobbyist and consultant for clients in New Orleans as well as statewide and nationally.[3]

Braden died of congestive heart failure in a New Orleans hospital at the age of sixty-eight. His survivors included his wife, Michele, and four children, Heidi, Remi, Hal, and Nick, and grandson Jack Cooper.[3] Remi Braden is the director of public affairs for the New Orleans Police Department.[1]

New Orleans journalist Clancy DuBos said of Braden: "Hank loved politics and public service and was among the most insightful politicians I have ever covered.".[1]